Let R be a plane region with area A whose boundary is a piecewise smooth, simple, closed curve C. The centroid (x, y) of the region is given by 1 x = 2/₁ f x²dy and ÿ = − 2₁ fy²dx. X - C 2A C Use the formulas above to find the centroid of the shaded region. NOTE: Enter the exact answer. (x, y) = (?, ?) 1 y y = x y = x³

Q: A find the dy dx y = (x²1nx)4

A:

Q: 2. Find the area of the plane figure bounded by the curves. Plot the graphs of the given functions,…

A:

Q: Evaluate ff, (F n) dS in the following cases: (a) F = (2y+z, x+z, y − x) and S is the portion of the…

A: (a)

Q: Directions: Find the function f(t) given the following information: f"(t) = sin(t) + cos(t) f(t) =…

A: Given Function:- f''t=sint+cost

Q: The point P, on the surface z? = (x – 27)y + 1, is the closest point to the origin. Find the…

A:

Q: Find the highest and lowest point of the surface z2 = x2 + y2 ,on the plane 4x – 3y + 8z = 10 %3D…

A:

Q: Find Ix, Iy, Io, x, and for the lamina bounded by the graphs of the equations. y = √√x, y = 0, x =…

A:

Q: Evaluate X J₁ sin (y + 2 x R where R is the triangular region with vertices (0,0), (0, 1), and…

A:

Q: Q. Let S = {(x,y), 2² + y? = 1} C R?, then S is homeomorphic to a. {(x, y), 22 -y2 = 1} b. {(x,y),…

A: Answer

Q: 1. Let F(x, y,z) = (x + y², y + z²,z + x²). Let C be the triangle with vertices (1,0,0), (0,1,0),…

A: Consider the provided question,

Q: Let R be the region bounded by the x-axis and the parabolas y2 = 64 x=u²v², y = 2uv to evaluate OA.…

A: is the region bounded by the axis and the parabolas  and

Q: Use the map G(u, v) = a = 4, b = 8, c = 6. b J D a y=cx uv v+1' v+1 (x + y) dx dy = to compute f (x…

A:

Q: Evaluate f. F.dr where F(x, y, z) = xyi + (x + y)j + x²k along the line segment from: A (1,3,1) to B…

A:

Q: Find I, Iy, Io, X, andy for the lamina bounded by the graphs of the equations. y = √√√x, y = 0, x =…

A: Given that the equations is:                                To find: for the lamina bonded by the…

Q: Calculate 5 d.S for the surface S: y = 4-z², 0≤x≤z≤2 (Express numbers in exact form. Use symbolic…

A: Solution is uploaded below

Q: Y = 3.065 x + (-35.96)=0.6451x + 46.92 an/Fear medial ing au of a t from asur oxim bial hat se toc…

A: Y= 3.065x + (-35.96) = 0.6451x + 46.92 We have to find value of f(x)

Q: • Consider the surface given by the equation (r- 1)² + (y+3)2 - (z-2)² = 1. Which of the following…

A: We have to find y- intercept.

Q: Find I, I, I, X, and y for the lamina bounded by the graphs of the equations. y = √√√x, y = 0, x =…

A: The region is bounded  by The graph of region

Q: Evaluate F. dr where F(x, y) = x²y² + 2xyj and C is the boundary of the square (clockwise) through…

A:

Q: 6. Find the area of the part of the surface z = x²-y², which lies in the first octant that is inside…

A: The solution is given by

Q: Evaluate z* + x dS where S is the cylinder x2 + y? = 36 between the planes z = -3 and z = 1,…

A:

Q: Let S be the surface in R³ defined by the equation x4. y5 - 5z = 8. Find a real-valued function g…

A:

Q: Given P (8, 0) and Q (0, -6). The perpendicular bisector of PQ meets the axis of the axis at A and…

A: The points are P(8,0) and Q(0,-6)

Q: 1. Let F = (vi-x)/(x² + y²), evaluate § ♬ dr, where C is circle (x − 1)² + (y − 1)² = r² with 0 <r…

A: We are given that          F = (y i - x j)/(x2 + y2)   Now, r = x i + y j       =&gt; dr = dx i + dy…

Q: Evaluate [[.(y+2/10 – z ) dS, where S is the surface cut from the par aboloid y +4z =36 by the…

A: Surface integral of a function f(x,y,z) on the surface S given by z=g(x,y) can be found by  ∫∫S…

Q: Find the derivative of f (y) = 4 sin? (y4). %3D

A:

Q: Estimate zx (0.50, 0) and zx (0, 1.0) and zy (0, 1.0) from the contour diagram for z (x, y) in the…

A: z(0.50,0) = 1z(0.75,0) = 2z(0.50,1) = 1z(0,1) = 1z(0,1.2) = 3z(0,1) = 1